The BioPace cranks were available since 1983 and were pretty heavily marketed during the mid-1980s. And, even SEVEN-speed freewheels had came out quite early [1980 (Suntour) and 81 (Shimano)]... although a 6-speeds remained common for quite a while with triple crank sets. So, the bike could easily be well over 20 years old - or at least the main part of your drive train
Best way to date the bike accurately would be to check the base of your seatpost for a two-digit date code and also look for very tiny two-digit letters on any of the Shimano components which are also date codes.
Since you got the bike used, the guess the frameset could actially be newer... and just built up with the guys old discarded junk components when he was selling it.
Ahem! 
Please?